Hypersonic Boundary-Layer Instabilities due to Near-Critical Roughness

Abstract

Measurements of instability and transition were obtained in the wake of a cylindrical roughness within the laminar nozzle-wall boundary layer of the Purdue Mach-6 Quiet Tunnel. Using wall-mounted pressure transducers along the wake centerline, the root-mean-square pressure and power spectra were computed to find evidence of instabilities within the roughness wake. The roughness height was adjusted to explore the case of incipient transition on the nozzle wall. It appeared that small variations in the experimental parameters could have a large effect on transition for the near-critical case. Several dominant disturbance frequencies were identified for a selected set of conditions. These disturbances appear to be due to instabilities developing within the wake of the roughness. The streamwise evolution of these disturbances are reported, as well as the spanwise distribution at one streamwise location within the wake. The experimentally observed disturbances can be used as a test case to continue to develop methods for computing the stability of roughness wakes. Nomenclature D = cylindrical roughness diameter, mm k = cylindrical roughness height, mm p 0 = tunnel stagnation pressure, kPa p 0 = fluctuating component of pressure, kPa Re k = roughness Reynolds number, ρ k u k k∕μ k Re k;crit = critical roughness Reynolds number Re ∞ = unit freestream Reynolds number, 1∕m T driver = temperature from a thermocouple at the upstream end of the driver tube, K T nozzle = mean temperature recorded by the thermocouples on the nozzle, K T 0 = tunnel stagnation temperature, K t = time after the diaphragm burst, s x = streamwise distance downstream from the central axis of the roughness, mm z = spanwise arc length from the center of the roughness, mm δ = boundary-layer thickness, defined as the height where the local velocity is 99.5% of the freestream value Subscripts i = initial condition k = roughness height condition ∞ = freestream condition

Computations of Disturbance Amplification Behind Isolated Roughness Elements and Comparison with Measurements

“…According to the measurements by Wheaton and Schneider, 37 the nozzle wall boundary layer remains completely laminar at k = 2.54 mm and, hence, that case corresponds to a subcritical roughness height. Measurements indicated that k = 2.79 mm (Re kk = 355) may be regarded as a near-critical height since, for this height, incipient transition is observed near the downstream end of the apparatus.…”

“…The first roughness configuration models the experiment by Wheaton and Schneider 37 for roughness heights that are post critical but well below the effective roughness height. The roughness element consists of a 5.97 mm diameter micrometer head that is mounted vertically at a distance of x = 1.924 meters from the nozzle throat in the BAMQT at Purdue University (Fig.…”

“…12-39 for additional recent findings in this area. This body of work includes stability of roughness wakes, 15,19,32 numerical simulations, 11,18,20,24,27,29,[33][34][35][36]38,39 wind tunnel experiments, 12,21,23,25,26,28,30,31,37 ballistic range experiments, 22 and flight measurements. 13,17 A review of work predating the abovementioned references was presented by Schneider.…”

“…To that end, computations are performed for a circular roughness element in the Mach 6 Boeing/AFOSR Mach-6 Quiet Tunnel (BAMQT) wind tunnel facility at Purdue University. Because of the intrinsic difficulties with hot wire measurements at high Mach numbers, the experimental measurements in the Mach 6 case are necessarily more limited than the Mach 3.5 database by Kegerise et al 5 Yet, the available measurements by Wheaton 30 and Wheaton and Schneider 37 are shown to yield useful insights via comparisons with the computational predictions. The second configuration of interest involves a roughness element with planform corresponding to a right-angled triangle in a Mach 3.5 flat plate boundary layer, which enables comparisons with the detailed measurements of Kegerise et al 5 An outline of this paper is as follows.…”

Pressure gradient effects on wake-flow instabilities behind isolated roughness elements on re-entry capsules

“…An extensive summary of experimental work, which focuses on roughnessrelated transition in hypersonic boundary layers on blunt bodies, is given by Reda 8 and Schneider. 15 The mechanisms leading to transition behind a three-dimensional roughness are only partly understood, but work on mainly super-and hypersonic roughness-induced transition (carefully conducted experiments, 16,17 extensive DNS simulations [18][19][20][21][22] and results from global, 23 two-dimensional linear eigenvalue (LST-2D) [24][25][26][27] and three-dimensional parabolized (PSE-3D) 18,28 instability analyses) have considerably increased the knowledge in the recent years. However, most investigations have been performed on flat plates with a zero pressure gradient (ZPG) and a detailed study on the influence of different pressure gradients on roughness wake-flow instabilities is still missing.…”